Multi-value microstructural descriptors for complex materials: analysis of ground states

We propose and analyze a multi-scale and multi-field description of complex materials in which we consider every material element as a system composed by $Qinmathbb{N}$ indistinct substructures. We pay attention to the equilibrium configurations of such bodies. We consider first rigid bodies with microstructure represented by means of $Q-$valued maps from the reference place to the manifold of microstructural shapes. In that case, just microenergetics appears. Then, we enlarge the stage considering large strains and energies of Ginzburg-Landau type with respect to the microstructural descriptor fields. In both cases we provide conditions for semicontinuity of the relevant energies and the existence of ground states.